According to the founding fathers of recent hypothesis testing the meaning of \(p\)  is the following [1]}: If the \(p\) -value falls below a predefined threshold of, say, \(\alpha \)  one should act as if the null hypothesis is false. On this behavioral strategy it is ensured that in the long run the type I error rate will be only \(\alpha \) . One may regret that this meaning implies only little for each individual measurement. However, given that the \(p\) -value arises in the frequentist framework its meaning has to be frequentist as well. All of the above misconceptions try to derive quantitative information from an individual trial already, which contradicts the underlying frequentist (i.e. “in the long run") conception.
